J. Hein, T. Jiang, L. Wang, and K. Zhang. On the complexity of comparing evolutionary trees. Discrete Applied Mathematics, 71:153--169, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....in the bound for the degree. Moreover both problems are NP hard for instances containing three trees of unbounded degree, hence it is necessary to focus on designing polynomial time approximation algorithms. The approximation complexity of the MHT problem has been deeply investigated in [21], where some strong negative results have been obtained. Since the MIT is a di erent restriction of the MIWT, it seems natural to investigate if the negative results for MHT hold also for MIT or the latter problem is easier to approximate than the former one. In our paper we show that the negative ....

....strong negative results have been obtained. Since the MIT is a di erent restriction of the MIWT, it seems natural to investigate if the negative results for MHT hold also for MIT or the latter problem is easier to approximate than the former one. In our paper we show that the negative results of [21] hold also for the MIT problem, as a consequence of a nontrivial application of the selfimprovement technique. Applying self improvement usually leads to a result of the form either problem admits a PTAS or cannot be approximated within a constant factor unless NP=P (or another unlikely ....

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J. Hein, T. Jiang, L. Wang, and K. Zhang. On the complexity of comparing evolutionary trees. Discrete Applied Mathematics, 71:153-169, 1996.

....of Canterbury, New Zealand. m.steel math.canterbury.ac.nz 1 . establish a relationship between the number of tree bisection and reconnection operations required to transform one tree into another and the size of the maximum agreement forest for the two trees, thereby correcting an error in [6]; investigate the computational complexity of the NNI, SPR and TBR Distance Problems, and point out that the TBR Distance Problem is NP hard; show that, for the tree bisection and reconnection operation, the question of whether a given unrooted binary tree can be transformed to another ....

.... are that (i) they form the basis of tree reconstruction heuristics that attempt to locate the best tree according to various criteria (see [9] and (ii) one of the tree edit operations, the SPR, is useful for modelling horizontal gene transfer and recombination events (see [3] 4] 5] [6] and [8] However before we investigate any tree edit operations, we need to introduce technical definitions. Definitions 1. An unrooted binary phylogenetic tree (or more briefly a binary tree) is a tree whose leaves (degree 1 vertices) are labelled bijectively by a (species) set S, and such ....

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J. Hein, T. Jiang, L. Wang, and K. Zhang, On the complexity of comparing evolutionary trees. Discr. Appl. Math., 71, 153--169 (1996).

....forest of these trees. Informally, the number of components of an agreement forest tells how many edges need to be cut from each of T and U so that the resulting forests agree, after performing some forced edge contractions. This problem is known to be NP hard. It was introduced by Hein et al. [3], who presented an approximation algorithm for it, claimed to have approximation ratio 3. We present here a 3 approximation algorithm for this problem and show that the performance ratio of Hein s algorithm is 4. 1 Introduction Phylogenetic trees or phylogenies are a standard model for ....

....are presented by Allen and Steel [1] In particular, they show that the size of a maximum agreement forest of two trees is precisely the TBR distance between them. We are concerned here with the problem of nding the size of a maximum agreement forest of two trees, which is known to be NP hard [3, 1]. The formal de nition of this problem is given in the next section. We present a 3approximation algorithm for this problem and show that a previous algorithm by Hein et al. 3] claimed to have performance ratio 3, has performance ratio 4. The algorithm we shall describe is simple, but the ....

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J. Hein, T. Jiang, L. Wang, and K. Zhang. On the complexity of comparing evolutionary trees. Discrete Applied Mathematics, 71:153-169, 1996.

....trees to find their similarities (e.g. agreement or consensus) and dissimilarities, i.e. distance, is thus an important issue in computational molecular biology. The nearest neighbor interchange (nni) distance [25, 24, 32, 4, 5, 3, 16, 17, 19, 29, 20, 21, 23] and the subtree transfer distance [12, 13, 15] are two major distance metrics that have been proposed and extensively studied for different reasons. Despite their many appealing aspects such as simplicity and sensitivity to tree topologies, computing these distances has remained very challenging. This article studies the complexity and ....

....to another. Figure 3 shows a subtree transfer operation and its corresponding recombination event. The parsimony model in [12, 13] requires the computation of the subtree transfer distance between two trees, i.e. the minimum number of subtrees we need to move to transform one tree into the other. [15] shows that computing the subtree transfer distance is NP complete and gives a simple approximation algorithm with ratio 3. It is relevant in practice to discriminate among subtree transfer operations as they occur with different frequencies. For example, it is reasonable to assume that sequences ....

J. Hein, T. Jiang, L. Wang, and K. Zhang, On the complexity of comparing evolutionary trees, Proc. 6th Combinatorial Pattern Matching Conf., Helsinki, 1995.

....1 Introduction An evolutionary tree models how different species in a given set have evolved. The leaves in an evolutionary tree correspond to species and internal nodes represent the species ancestors. The problem of constructing a reliable evolutionary tree has been studied a lot recently [2, 3, 4, 7, 8, 14, 13, 16, 17, 19, 20]. There are many different approaches, depending among other things on what kind of data that is available. Therefore, various versions of this problem arise in, for example, computational biology when one wants to find out how different species are related, and comparative linguistics, where it ....

.... special case of MHT in which at least one of the given trees has bounded degree, there exist polynomial time algorithms [2, 16] In contrast, MHT is known to be NP complete even for instances with three trees of unbounded degree [16] The first non approximability result for MHT was published in [7]. It states that for three trees with unbounded degree, MHT cannot be approximated within ratio 2 log ffi n in polynomial time for any ffi 1 unless NP DTIME[2 polylog n ] Here we prove that, unless P=NP, MHT cannot be approximated within a factor of N ffl ; for any 0 ffl 1 9 in ....

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J. Hein, T. Jiang, L. Wang, and K. Zhang. On the Complexity of Comparing Evolutionary Trees. Discrete Applied Mathematics, 71, 1996, pp. 153-169.

....case prepares us for having the degree d as an exponent in our time complexity, it would be nice to reduce the time for finding the MWT to O(c d p(n; k) where p is a polynomial, rather than O(n d ) We presented here an approximation for the problem of finding the complement of the MHT. In [13] it was proven that the MHT problem for three trees with unbounded degree can not be approximated within ratio n ffl for any constant ffl 1. For the case of bounded degree trees, the time was improved by [5] From a graph theoretic aspect, it would be interesting to find a maximum agreement ....

....the time was improved by [5] From a graph theoretic aspect, it would be interesting to find a maximum agreement subtree in the sense of maximizing the number of edges, while using true contraction. The number is no less than n because every tree can be contracted to a star. However, again in [13] it was shown that this prolem is NP hard even for two trees. An ambitious problem is to define tree closeness metrics and efficiently find the closest tree to a set of trees keeping all the leaves. Acknowledgements We wish to thank Mike Steel for his great help in refining this paper, Bob ....

J. Hein, T. Jiang, L. Wang, and K. Zhang. On the complexity of comparing evolutionary trees. manuscript, 1995.

....1 Introduction An evolutionary tree models how different species in a given set have evolved. The leaves in an evolutionary tree correspond to species and internal nodes represent the species ancestors. The problem of constructing a reliable evolutionary tree has been studied a lot recently [2, 3, 4, 7, 8, 13, 15, 16, 18, 19]. There are many different approaches, depending on among other things what kind of data that is available. Therefore, various versions of this problem arise in, for example, computational biology when one wants to find out how different species are related, and comparative linguistics, where it ....

.... special case of MHT in which at least one of the given trees has bounded degree, there exist polynomial time algorithms [2, 15] In contrast, MHT is known to be NP complete even for instances with three trees of unbounded degree [15] The first non approximability result for MHT was published in [7]. It states that for three trees with unbounded degree, MHT cannot be approximated within ratio 2 log ffi n in polynomial time for any ffi 1 unless NP DTIME[2 polylog n ] Here we prove that, unless P=NP, MHT cannot be approximated within a factor of N ffl ; for any 0 ffl 1 9 in ....

[Article contains additional citation context not shown here]

J. Hein, T. Jiang, L. Wang, and K. Zhang. On the Complexity of Comparing Evolutionary Trees. Discrete Applied Mathematics, 71, 1996, pp. 153-169.

....species tree for a set of taxa given a set of (possibly contradictory) gene trees. Several models for attacking the problem have appeared in the literature including the famous maximum agreement subtree (MAST) FM67, NA86, PC97] The known models, which are related to agreement subtrees (see also [HJWZ95, HJWZ96] amongst others) or consensus trees (see for example [S91] are mathematical models but biologically rather meaningless. A biological cost model which has recently received considerable attention is the Gene Duplication and Loss Model suggested in biological terms in [GCMRM79] and discussed in ....

J. Hein, T. Jiang, L. Wang, and K. Zhang. "On the Complexity of Comparing Evolutionary Trees", DAMATH: Discrete Applied Mathematics and Combinatorial Operations Research and Computer Science 71 (1996).

....species tree for a set of taxa given a set of (possibly contradictory) gene trees. Several models for attacking the problem have appeared in the literature including the famous maximum agreement subtree (MAST) FM67, NA86, PC97] The known models, which are related to agreement subtrees (see also [HJWZ95, HJWZ96] amongst others) or consensus trees (see for example [S91] are mathematical models but biologically rather meaningless. A biological cost model which has recently received considerable attention is the Gene Duplication and Loss Model suggested in biological terms in [GCMRM79] and discussed in ....

J. Hein, T. Jiang, L. Wang, and K. Zhang. "On the Complexity of Comparing Evolutionary Trees", Proceedings of the 6th Annual Symposium on Combinatorial Pattern Matching, LNCS 937 (1995), pp. 177--190.

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J. Hein, T. Jiang, L. Wang, and K. Zhang. On the complexity of comparing evolutionary trees. Discrete Applied Mathematics, 71:153--169, 1996.

....Bhaskar DasGupta, Xin He, Tao Jiang, Ming Li, John Tromp, and Louxin Zhang Abstract. In the practice of molecular evolution, di#erent phylogenetic trees for the same group of species are often produced either by procedures that use diverse optimality criteria [24] or from di#erent genes [15, 16, 17, 18, 14]. Comparing these trees to find their similarities (e.g. agreement or consensus) and dissimilarities, i.e. distance, is thus an important issue in computational molecular biology. The nearest neighbor interchange (nni) distance [29, 28, 34, 3, 6, 2, 19, 20, 23, 33, 22, 21, 26] is a natural ....

J. Hein, T. Jiang, L. Wang, and K. Zhang, On the complexity of comparing evolutionary trees, Discrete Applied Mathematics 71, 153-169, 1996.

.... recombination [7, 8] Hein observed that the evolution of a sequence with k recombinations could be described by k recombination points and k 1 trees describing the evolution of the k 1 intervals, where two neighboring trees were either identical or differed by one subtree transfer operation [7, 8, 9, 3, 2]. A heuristic method was proposed to find the most parsimonious history of the sequences in terms of mutation and recombination operations. Another strike was given by Kececioglu and Gusfield [12] They introduced two new problems, recombination distance, and bottleneck recombination history. ....

J. Hein, T. Jiang, L. Wang, and K. Zhang, On the complexity of comparing evolutionary trees, Discrete Applied Mathematics, 71(1996), 153-169.

....trees to find their similarities (e.g. agreement or consensus) and dissimilarities, i.e. distance, is thus an important issue in computational molecular biology. The nearest neighbor interchange (nni) distance [26, 24, 32, 4, 5, 3, 16, 17, 19, 30, 20, 21, 23] and the subtree transfer distance [12, 13, 15] are two major distance metrics that have been proposed and extensively studied for different reasons. Despite their many appealing aspects such as simplicity and sensitivity to tree topologies, computing these distances has remained very challenging. This article studies the complexity and ....

....line in second row is 3. a subtree transfer operation and its corresponding recombination event. The parsimony model in [12, 13] requires the computation of the subtree transfer distance between two trees, i.e. the minimum number of subtrees we need to move to transform one tree into the other. [15] shows that computing the subtree transfer distance is NP complete and gives a simple approximation algorithm with ratio 3. It is relevant in practice to discriminate among subtree transfer operations as they occur with different frequencies. For example, it is reasonable to assume that sequences ....

J. Hein, T. Jiang, L. Wang, and K. Zhang, On the complexity of comparing evolutionary trees, Proc. 6th Combinatorial Pattern Maching Conf., Helsinki, 1995.

....of Waterloo. Work done while the author was at University of Waterloo. Abstract In the practice of molecular evolution, different phylogenetic trees for the same group of species are often produced either by procedures that use diverse optimality criteria [24] or from different genes [15, 16, 17, 18, 14]. Comparing these trees to find their similarities (e.g. agreement or consensus) and dissimilarities, i.e. distance, is thus an important issue in computational molecular biology. The nearest neighbor interchange (nni) distance [29, 28, 34, 3, 6, 2, 19, 20, 23, 33, 22, 21, 26] is a natural ....

J. Hein, T. Jiang, L. Wang, and K. Zhang, On the complexity of comparing evolutionary trees, Discrete Applied Mathematics 71, 153-169, 1996.

....i.e. the minimum number of subtrees we need 0 0 1 1 1 1 Figure 2: Recombination event between two sequences. The genetic material (thick lines) that is in one sequence after recombination, was in two sequences just before the recombination. to move to transform one tree into the other. In [15] the authors show that computing the subtreetransfer distance is NP complete and give a simple approximation algorithm with approximation ratio 3. It is relevant in practice to discriminate among subtree transfer operations as they occur with different frequencies. For example, it is reasonable to ....

J. Hein, T. Jiang, L. Wang, and K. Zhang, On the complexity of comparing evolutionary trees, Discrete Applied Mathematics 71, 153-169, 1996.

....sequences (rightmost tree in (b) a common ancestor of s 2 ; s 3 ; s 4 is found going back in time; hence the second number of the thick line in second row is 3. subtree transfer distance between two trees, i.e. the minimum number of subtrees we need to move to transform one tree into the other. [13] shows that computing the subtree transfer distance is NP complete and gives a simple approximation algorithm with ratio 3. It is relevant in practice to discriminate among subtree transfer operations as they occur with different frequencies. For example, it is reasonable to assume that sequences ....

J. Hein, T. Jiang, L. Wang, and K. Zhang, On the complexity of comparing evolutionary trees, Discrete Applied Mathematics 71, 153-169, 1996.

....2 shows such a subtree transfer operation. The subtree transfer distance, D st (T 1 ; T 2 ) between two trees T 1 s5 s1 s2 s3 s4 s1 s2 s4 one subtree transfer s3 s5 Figure 2: An example of subtree transfer. and T 2 is the minimum number of subtrees we need to move to transform T 1 into T 2 [19, 20, 22, 8, 7]. It is sometimes appropriate in practice to discriminate among subtreetransfer operations as they occur with different frequencies. In this case, we can charge each subtree transfer operation a cost equal to the distance (the number of nodes passed) that the subtree has moved in the current ....

J. Hein, T. Jiang, L. Wang, and K. Zhang, On the complexity of comparing evolutionary trees, Discrete Applied Mathematics, 71, pp. 153169, 1996.

....operation. The subtree transfer distance, D st (T 1 ; T 2 ) between two trees T 1 s5 s1 s2 s3 s4 s1 s2 s4 one subtree transfer s3 s5 Figure 3: An example of a subtree transfer operation on a tree. and T 2 is the minimum number of subtrees we need to move to transform T 1 into T 2 [34, 35, 36, 14, 15]. It is sometimes appropriate in practice to discriminate among subtreetransfer operations as they occur with different frequencies. In this case, we can charge each subtree transfer operation a cost equal to the distance (the number of nodes passed) that the subtree has moved in the current tree. ....

....and linear cost subtree transfer models can also be used as alternative measures for comparing evolutionary trees generated by different tree reconstruction methods. In fact, on unweighted phylogenies, the linear cost subtree transfer distance is identical to the nni distance [15] The authors in [36] show that computing the subtree transfer distance between two evolutionary trees is NP hard and give an approximation algorithm for this distance with performance ratio 3. 2.5 Rotation Distance Rotation distance is a variant of the nni distance for rooted, ordered trees. A rotation is an ....

[Article contains additional citation context not shown here]

J. Hein, T. Jiang, L. Wang, and K. Zhang. On the complexity of comparing evolutionary trees, Discrete Applied Mathematics, 71(1996), 153169.

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J. Hein, T. Jiang, L. Wang, and K. Zhang. On the complexity of comparing evolutionary trees. Discrete Applied Mathematics, 71:153--169, 1996.

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J. Hein, T. Jiang, L. Wang, and K. Zhang, "On the complexity of comparing evolutionary trees," Discrete Applied Mathematics, vol. 71, no. 1--3, pp. 153--169, 1996.

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J. Hein, T. Jiang, L. Wang, and K. Zhang, "On the complexity of comparing evolutionary trees," Discrete Applied Mathematics, vol. 71, no. 1--3, pp. 153--169, 1996.

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J. Hein, T. Jiang, L. Wang, and K. Zhang, "On the complexity of comparing evolutionary trees," Discrete Applied Mathematics, vol. 71, no. 1--3, pp. 153--169, 1996.

No context found.

J. Hein, T. Jiang, L. Wang, and K. Zhang. On the complexity of comparing evolutionary trees. Discrete Applied Mathematics, 71:153--169, 1996.

No context found.

J. Hein, T. Jiang, L. Wang, and K. Zhang. On the complexity of comparing evolutionary trees. Discrete Applied Mathematics, 71:153--169, 1996.

No context found.

J. Hein, T. Jiang, L. Wang, and K. Zhang. On the complexity of comparing evolutionary trees. Discrete Applied Mathematics, 71:153--169, 1996.

No context found.

J. Hein, T. Jiang, L. Wang, and K. Zhang. On the complexity of comparing evolutionary trees. Discrete Applied Mathematics, 71:153--169, 1996.

No context found.

J. Hein, T. Jiang, L. Wang, and K. Zhang. On the complexity of comparing evolutionary trees. Discrete Applied Mathematics, 71:153--169, 1996.

No context found.

J. Hein, T. Jiang, L. Wang, and K. Zhang. On the complexity of comparing evolutionary trees. Discrete Applied Mathematics, 71:153--169, 1996.

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J. Hein, T. Jiang, L. Wang, and K. Zhang. On the complexity of comparing evolutionary trees. In Z. Galil and E. Ukkonen, editors, Combinatorial Pattern Matching, pages 177--190. Springer, 1995.

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J. Hein, T. Jiang, L. Wang, and K. Zhang, On the complexity of comparing evolutionary trees, Discrete Appl. Math. 71 (1-3) (1996) 153--169.

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